**Core Concept**
Hirschsprung's disease is a congenital condition characterized by the absence of ganglion cells in the distal colon and rectum, leading to functional obstruction and chronic constipation. This condition is caused by a failure of neural crest cells to migrate to the distal gut during embryonic development.

**Why the Correct Answer is Right**
The absence of ganglion cells in the rectum, as confirmed by the rectal biopsy, is a hallmark of Hirschsprung's disease. This absence leads to an accumulation of stool in the rectum, causing distension and functional obstruction. The paucity of air in the rectum on abdominal radiography is consistent with this diagnosis. The symptoms of nausea and vomiting are secondary to the abdominal distension and obstruction.

**Why Each Wrong Option is Incorrect**
**Option A:** Ulcerative colitis is an inflammatory bowel disease characterized by chronic inflammation and ulcers in the colon, which is not consistent with the absence of ganglion cells in the rectum.

**Option B:** Intestinal obstruction due to a mechanical cause, such as intussusception or volvulus, would typically present with more acute symptoms and a different radiographic appearance.

**Option C:** Megacolon, also known as congenital megacolon, is a condition characterized by a large, dilated colon, but it is not necessarily associated with the absence of ganglion cells.

**Clinical Pearl / High-Yield Fact**
Hirschsprung's disease is a classic example of a congenital condition that can be diagnosed by a rectal biopsy showing an absence of ganglion cells.

**Correct Answer:** C.